How Accurately Can the Position of a Proton Be Determined at High Speeds?

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Homework Help Overview

The discussion revolves around determining the maximum accuracy of a proton's position when it is traveling at a high speed, specifically given a velocity of (6.560+0.012)*10^5 m/s. The subject area includes concepts from quantum mechanics, particularly the Uncertainty Principle, as well as considerations from relativistic physics.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants discuss the application of the Uncertainty Principle and its relation to momentum and position. There are considerations about the impact of velocity on accuracy, including whether relativistic effects need to be taken into account.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of how velocity affects the accuracy of position determination. Some guidance has been offered regarding the application of the Uncertainty Principle, but there is no explicit consensus on the approach to take.

Contextual Notes

There is mention of the proton's speed being around 10^5 m/s, which raises questions about whether relativistic effects are significant in this context. Participants are also considering the implications of using Newtonian mass versus relativistic mass.

Ve3Mike
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I have a question i am having trouble on. "A proton is traveling with a speed of (6.560+0.012)*10^5 m/s. With what maximum accurancy can its position be ascertained?" Any help will be appreciated.
 
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Go through your notes on the Uncertainty Principle. There is an equation relating uncertainty in momentum (mass x velocity) and position that can be directly applied.
 
Hi,

The accuracy actually depends upon the velocity. You have first got to ascertain the shell by which it travels and use relativity to find the increase in mass due to the high velocity and then you may use the mass*velocity equation.

gagsrcool
 
At ~10^5 m/s, the proton is non-relativistic and the Newtonian mass is accurate enough.
 

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